Novel nonstandard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational algorithm for the determination of the dimension of line-bundle-valued cohomology groups on toric varieties. Applications to...

Novel nonstandard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational algorithm for the determination of the dimension of line-bundle-valued cohomology groups on toric varieties. Applications to the computation of chiral massless matter spectra in string compactifications are discussed, and using the software package cohomCalg, its utility is highlighted on a new target space dual pair of (0,2) heterotic string models. Minimize

The content of this thesis was generated during the past twelve months. A lot of people supported me during that time in different ways. Firstly I would like to thank Prof. Olaf Lechtenfeld and the Institut für Theoretische Physik for giving me the opportunity to write my “Diplomarbeit ” in this institute and making it possible for me to go to s...

The content of this thesis was generated during the past twelve months. A lot of people supported me during that time in different ways. Firstly I would like to thank Prof. Olaf Lechtenfeld and the Institut für Theoretische Physik for giving me the opportunity to write my “Diplomarbeit ” in this institute and making it possible for me to go to summer schools and conferences during that period where I have been able to widen my knowledge as well as to get in touch with many other students working on similar fields. Special gratitude I want to express to Dr. Alexander D. Popov, who has chosen the specific task I worked on in the last year, guided me through the wide range of mathematics needed, spent a lot of time reading my drafts of the thesis and answered a lot of questions in various discussions and e-mails. I am also thankful for his advice concerning more general issues not always directly related to the task itself. I also want to thank Prof. Olaf Lechtenfeld for several helpful discussions concerning mostly specific questions about the topic. I am also grateful to Dr. Tatiana A. Ivanova for carefully checking my calculations as well as useful remarks on my thesis and of course for a good collaboration. Furthermore I would like to thank my colleagues Kirsten Vogeler, Anne Müller-Lohmann Minimize

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on spaces of the form R × SU(3)/H, with H equals either SU(2) × U(1) or U(1) × U(1). For the corresponding quiver gauge theory we derive the equations of motion and construct some specific solutions for the Higgs fields using different gauge groups. Specifically we choose t...

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on spaces of the form R × SU(3)/H, with H equals either SU(2) × U(1) or U(1) × U(1). For the corresponding quiver gauge theory we derive the equations of motion and construct some specific solutions for the Higgs fields using different gauge groups. Specifically we choose the gauge groups U(6) and U(8) for the space R×CP 2 as well as the gauge group U(3) for the space R×SU(3)/U(1)×U(1), and derive Yang-Mills equations for the latter one using a spin connection endowed with a nonvanishing torsion. We find that a specific value for the torsion is necessary in order to obtain non-trivial solutions of Yang-Mills equations. Finally, we take the space R × CP 1 × CP 2 and derive the equations of motion for the Higgs sector for a U (3m + 3) gauge theory. 1 Introduction and summary The Yang-Mills equations in more than four dimensions naturally appear in the low-energy limit of superstring theory. Furthermore, natural BPS-type equations for gauge fields in dimensions d> 4, introduced in [1, 2], also appear in superstring compactifications as the conditions for survival of at least one supersymmetry in low-energy effective field theory in four dimensions [3]. Some solutions Minimize

We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R×G/H. On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang-Mills equations to φ 4-ki...

We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R×G/H. On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang-Mills equations to φ 4-kink equations on R. Depending on the boundary conditions and torsion, we obtain solutions to the Yang-Mills equations describing instantons, chains of instanton-anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on R × G/H, dyon-type configurations are constructed as well. We also present explicit solutions to the Yang-Mills flow equations and compare them with the Yang-Mills solutions on R × G/H.1 Introduction and summary The Yang-Mills equations in more than four dimensions naturally appear in the low-energy limit of superstring theory. Furthermore, natural BPS-type equations for gauge fields in dimensions d> 4, introduced in [1, 2], also appear in superstring compactifications as the conditions for the survival of at least one supersymmetry in low-energy effective field theory in four dimensions [3]. Minimize

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on spaces of the form R x SU(3)/H, with H equals either SU(2) x U(1) or U(1) x U(1). For the corresponding quiver gauge theory we derive the equations of motion and construct some specific solutions for the Higgs fields using different gauge groups. Specifically we choose t...

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on spaces of the form R x SU(3)/H, with H equals either SU(2) x U(1) or U(1) x U(1). For the corresponding quiver gauge theory we derive the equations of motion and construct some specific solutions for the Higgs fields using different gauge groups. Specifically we choose the gauge groups U(6) and U(8) for the space R x CP^2 as well as the gauge group U(3) for the space R x SU(3)/U(1)xU(1), and derive Yang-Mills equations for the latter one using a spin connection endowed with a non-vanishing torsion. We find that a specific value for the torsion is necessary in order to obtain non-trivial solutions of Yang-Mills equations. Finally, we take the space R x CP^1 x CP^2 and derive the equations of motion for the Higgs sector for a U(3m+3) gauge theory. ; Comment: 21 pages, 4 figures; v2: figures added, references updated, published version (JMP) Minimize

In this article we summarize and extend the ideas and investigations on so called target space dualities of heterotic models with (0,2) worldsheet supersymmetry as they were partly presented on the String-Math 2011 conference. After the generic description of the duality, we give some novel examples involving vector bundles that are not deformat...

In this article we summarize and extend the ideas and investigations on so called target space dualities of heterotic models with (0,2) worldsheet supersymmetry as they were partly presented on the String-Math 2011 conference. After the generic description of the duality, we give some novel examples involving vector bundles that are not deformations of the tangent bundle but more generic ones corresponding to SO(10) and SU(5) gauge theories in four dimensions. We show explicitly that the necessary conditions for a duality also hold for compactifications of this kind. Finally we will present the results of the large landscape scan of E_6 models. ; Comment: 10 Pages, 2 Tables, Contribution to the String-Math 2011 Proceedings Minimize

In the framework of (0,2) gauged linear sigma models, we systematically generate sets of perturbatively dual heterotic string compactifications. This target space duality is first derived in non-geometric phases and then translated to the level of GLSMs and its geometric phases. In a landscape analysis, we compare the massless chiral spectra and...

In the framework of (0,2) gauged linear sigma models, we systematically generate sets of perturbatively dual heterotic string compactifications. This target space duality is first derived in non-geometric phases and then translated to the level of GLSMs and its geometric phases. In a landscape analysis, we compare the massless chiral spectra and the dimensions of the moduli spaces. Our study includes geometries given by complete intersections of hypersurfaces in toric varieties equipped with SU(n) vector bundles defined via the monad construction. ; Comment: 40 pages, 6 figures Minimize

We present a proof of the algorithm for computing line bundle valued cohomology classes over toric varieties conjectured by R.~Blumenhagen, B.~Jurke and the authors (arXiv:1003.5217) and suggest a kind of Serre duality for combinatorial Betti numbers that we observed when computing examples. ; Comment: Download of the implementation in C++: http...

We present a proof of the algorithm for computing line bundle valued cohomology classes over toric varieties conjectured by R.~Blumenhagen, B.~Jurke and the authors (arXiv:1003.5217) and suggest a kind of Serre duality for combinatorial Betti numbers that we observed when computing examples. ; Comment: Download of the implementation in C++: http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg Minimize